pubs.acs.org/Langmuir © 2009 American Chemical Society
Complex Micelles from Self-Assembly of ABA Triblock Copolymers in B-Selective Solvents Weixin Kong, Baohui Li,* Qinghua Jin, and Datong Ding School of Physics and Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, Tianjin, 300071, China
An-Chang Shi* Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada Received September 2, 2009. Revised Manuscript Received October 22, 2009 We report an extensive simulation study of the self-assembly of amphiphilic ABA triblock copolymers dissolved in solvents selective for the middle B-block. The effects of copolymer composition, copolymer concentration, and Asolvent interactions on the morphologies and morphological transitions of the aggregates are examined systematically. The simulations reveal that a rich variety of aggregates, ranging from spherical and rodlike micelles and vesicles to toroidal and net-cage micelles, can be formed spontaneously from a randomly generated initial state. Phase diagrams are constructed and rich morphological transitions are predicted. Chain packing in different micelles is investigated. The simulation results are compared with previous observations or predictions for related copolymer systems.
Introduction The self-assembly of amphiphilic block copolymers in a dilute solution has attracted much scientific interest because of the formation of a variety of aggregates and potential applications of these aggregates in technical and especially biomedical areas.1 In the past years, the self-assembly of AB diblock copolymer solutions, the simplest case of block copolymer solutions, has been extensively investigated.2-18 Usually, their micellization in block selective solvents produces core-corona micelles, where the insoluble block forms the compact core and the soluble block forms the swollen corona of the resultant core-corona structure. The specific size and shape of the micelle were attributed to a balance of three contributions to the free energy of the system: chain stretching in the core, the interfacial energy, and repulsion *To whom correspondence should be addressed. E-mail: baohui@nankai. edu.cn;
[email protected]. (1) Riess, G. Prog. Polym. Sci. 2003, 28, 1107. (2) Jain, S.; Bates, F. S. Macromolecules 2004, 37, 1511. (3) Jain, S.; Bates, F. S. Science 2003, 300, 460. (4) Raez, J.; Manners, I.; Winnik, M. A. J. Am. Chem. Soc. 2002, 124, 10381. (5) Won, Y.-Y.; Brannan, A. K.; Davis, H. T.; Bates, F. S. J. Phys. Chem. B 2002, 106, 3354. (6) Lodge, T. P.; Pudil, B.; Hanley, K. J. Macromolecules 2002, 35, 4707. (7) Forster, S.; Berton, B.; Hentze, H.-P.; Kramer, E.; Antonietti, M.; Lindner, P. Macromolecules 2001, 34, 4610. (8) Schuch, H.; Klingler, J.; Rossmanith, P.; Frechen, T.; Gerst, M.; Feldthusen, J.; Muller, A. H. E. Macromolecules 2000, 33, 1734. (9) Won, Y.-Y.; Davis, H. T.; Bates, F. S. Science 1999, 283, 960. (10) Nakano, M.; Matsuoka, H.; Yamaoka, H.; Poppe, A.; Richter, D. Macromolecules 1999, 32, 697. (11) Yu, Y.; Zhang, L.; Eisenberg, A. Macromolecules 1998, 31, 1144. (12) Yu, K.; Eisenberg, A. Macromolecules 1998, 31, 3509. (13) Zhang, L.; Eisenberg, A. Science 1995, 268, 1728. (14) Zhang, L. F.; Bartels, C.; Yu, Y. S.; Shen, H. W.; Eisenberg, A. Phys. Rev. Lett. 1997, 79, 5034. (15) Yu, Y.; Zhang, L. F.; Eisenberg, A. Langmuir 1996, 12, 5980. (16) Prochazka, K.; Martin, T. J.; Munk, P.; Webber, S. E. Macromolecules 1996, 29, 6518. (17) Zhang, L. F.; Eisenberg, A. J. Am. Chem. Soc. 1996, 118, 3168. (18) Huang, H.; Chung, B.; Jung, J.; Park, H.-W.; Chang, T. Angew. Chem., Int. Ed. 2009, 48, 4594. (19) Choucair, A.; Eisenberg, A. Eur. Phys. J. E 2003, 10, 37.
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among coronal chains.19,20 Changing any one of the factors that affect these three terms (such as the block length of the copolymer, or the initial concentration of the polymer, or the presence of additives such as salts, acids, bases, etc.) disturbs the force balance governing the size and shape of micelles, which can lead to the transformation of one morphology into another. Therefore, the size and shape of micelles can, in principle, be precisely tuned. On the other hand, block copolymer micelles can exhibit a rich variety of morphologies. For example, spheres, rods, vesicles, tubules, needles, lamellae, cylindrical networks, hollow hoop, ring-shaped toroidal micelles, large compound micelles, and various mixed morphologies have been observed in AB diblock copolymer dilute solutions.2-20 Because of this morphology variety and complexity, fine-tuning the size and shape of block copolymer micelles experimentally remains a challenge. In addition, a feature shared by the self-assembly of block copolymers in a dilute solution is the coexistence of disparate morphologies even in one experimental system.21,22 The reason for the coexistence of the disparate morphologies remains an open problem. The self-assembly of ABA-type triblock copolymers in solvents selective for the outer (A) blocks has been extensively investigated both experimentally and theoretically in the past few years.23-29 Studies reveal that these triblock copolymer solutions also present rich micellar morphologies, which follow basically the same rules as that for AB diblock copolymer solutions. In contrast, micelles from another type of ABA triblock copolymer solutions, in which the solvent is selective for the middle (B) block, are relatively less (20) (21) (22) 2728. (23) (24) (25) (26) (27) (28) (29)
Soo, P. M.; Eisenberg, A. J. Polym. Sci., Part B: Polym. Phys. 2004, 42, 923. Disher, D. E.; Eisenberg, A. Science 2002, 297, 967. Shen, H. W.; Zhang, L. F.; Eisenberg, A. J. Am. Chem. Soc. 1999, 121, Zhu, J.; Liao, Y.; Jiang, W. Langmuir 2004, 20, 3809. Jiang, Y.; Zhu, J.; Jiang, W.; Liang, H. J. J. Phys. Chem. B 2005, 109, 21549. Zhu, J.; Yu, H. Z.; Jiang, W. Macromolecules 2005, 38, 7492. Zhu, J.; Jiang, Y.; Liang, H.; Jiang, W. J. Phys. Chem. B 2005, 109, 8619. Zhu, J; Jiang, W. Macromolecules 2005, 38, 9315. Du, H.; Zhu, J.; Jiang, W. J. Phys. Chem. B 2007, 111, 1938. Li, X.; Deng, M.; Liu, Y.; Liang, H. J. J. Phys. Chem. B. 2008, 112, 14762.
Published on Web 11/04/2009
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studied.30 In this case, the middle B-block can be bridged with the outer A-blocks located in different micellar cores, which is a case quite different from that in A-selective solvents. ABA triblock copolymers with small solvophobic end blocks have been investigated for several years as systems forming associative networks of flowerlike micelles, which at high concentrations result in formation of elastic gels.31 Both experiments and simulations have shown that block sequence does have an effect on the micellization or gelation of triblock copolymer solutions.32,33 However, the phase behavior and chain conformations of ABA-type triblock copolymers in B-selective solvents remain much less understood. In the present study, we fill in this gap by carrying out an extensive simulation investigation of the self-assembly of amphiphilic ABA triblock copolymers in solvents selective for the middle B-block. The simulations reveal that a rich variety of complex aggregates, depending on the polymer composition, copolymer concentration, and A-solvent interactions, can be formed spontaneously from a randomly generated initial state. Morphological transitions including vesicles and several types of toroidal micelles are predicted. Furthermore, chain packing in different micelles is investigated.
Model and Method The computer simulations were carried out using a simulated annealing method,34,35 which is a well-known procedure for obtaining the lowest-energy “ground states” in complex systems. The copolymers were modeled by the single-site bond fluctuation model of Carmesin and Kremer36 and of Larson.37 Previous studies on this model system have established that this approach provides an efficient methodology for studying the self-assembly of block copolymers in solutions38 or in confined environments.39 For completeness, the model and algorithm are briefly reviewed below, whereas a detailed description can be found elsewhere.38 Model triblock copolymers consist of linear chains composed of A and B monomers, AnBN-2nAn, where 2n and N are the number of A-monomers and that of all monomers, respectively. In each simulation, NCh chains of model triblock copolymers AnBN-2nAn were embedded in a simple cubic lattice of volume V = L L L with L = 60. Periodic boundary conditions are applied to all three directions. The initial configuration is generated by randomly creating NCh triblock copolymer chains on the lattice, where each monomer occupies one lattice site and two consecutive monomers pffiffiffi are connected by bonds that can adopt the lengths of 1 and 2. Thus each lattice site has 18 nearest neighbor sites. The copolymers are assumed to be self-avoiding, that is, no two monomers can occupy the same site simultaneously. After the desired number of copolymer chains has been generated, the unoccupied sites are designated as solvent molecules where each solvent molecule occupies one lattice site. The copolymer concentration is defined as cp = NNCh/V. Only the exchange movement of monomers is used in the simulations.38 In an exchange move, a monomer is selected, and it can exchange with a solvent molecule epanek, (30) Giacomelli, F. C.; Riegel, I. C.; Petzhold, C. L.; da Silveira, N. P.; St P. Langmuir 2009, 25, 731. (31) Agrawal, S. K.; Sanabria-DeLong, N.; Tew, G. N.; Bhatia, S. R. Macromolecules 2008, 41, 1774 and references herein. (32) Hoogenboom, R.; Wiesbrock, F.; Huang, H.; Leenen, M. A. M.; Thijs, H. M. L.; van Nispen, S. F. G. M.; van der Loop, M.; Fustin, C. A.; Jonas, A. M.; Gohy, J. F.; Schubert, U. S. Macromolecules 2006, 39, 4719. (33) Kim, S. H.; Jo, W. H. Macromolecules 2001, 34, 7210. (34) Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P., Jr. Science 1983, 220, 671. (35) Grest, G. S.; Soukoulis, C. M.; Levin, K. Phys. Rev. Lett. 1986, 56, 1148. (36) Carmesin, I.; Kremer, K. Macromolecules 1988, 21, 2819. (37) Larson, R. G. J. Chem. Phys. 1989, 91, 2479; 1992, 96, 7904. (38) Sun, P.; Yin, Y.; Li, B.; Chen, T.; Jin, Q.; Ding, D.; Shi, A.-C. J. Chem. Phys. 2005, 122, 204905. (39) Yu, B.; Sun, P.; Chen, T.; Jin, Q.; Ding, D.; Li, B.; Shi, A.-C. Phys. Rev. Lett. 2006, 96, 138306.
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on one of its 18 nearest neighbors. If the exchange does not break the chain, it is allowed. If the exchange creates a single break in the chain, the vacancy will continue to exchange with subsequent monomers along the broken chain until reconnection of the links occurs. If the exchange breaks the chain into more than two parts, it is not allowed. The acceptance or rejection of the attempted move is further governed by the Metropolis rule.40 The energy of the system is the objective function of the simulated annealing procedure. In the present paper only the 18 nearest neighbor interactions are considered, which are modeled by assigning an energy Eij =εijkBTref to each nearest neighbor pair of unlike components i and j, where i, j = A, B, and S (solvent); εij is the reduced interaction energy; kB the Boltzmann constant; and Tref is a reference temperature. It is assumed that εii = 0, with i = A, B, and S. The annealing were carried out using a linear schedule, Ti = fTi-1, where Ti is the temperature used in the ith annealing step and f is a scaling factor. The annealing was continued until the number of the annealing steps reached a predetermined value. Specifically, the initial temperature was set at T1 = 120Tref and 130 annealing steps were used. The scaling factor f was taken as 0.95 or 0.99, depending on the difference of the average energies of the system at the previous two annealing steps; f = 0.95 was used when the difference of the average energy is small, and f = 0.99 was used when the average energy difference is large. At each annealing step, 9000 Monte Carlo steps (MCS) are performed. One MCS is defined as the time taken for, on average, all the lattice sites to be visited for an attempted move. For all the simulations reported in this paper, the number of monomers in each chain is fixed at N = 24. The copolymers employed in our studies consist of two solvophobic (A) outer blocks and one solvophilic (B) middle block. The amphiphilic nature of chains are enforced by keeping εBS = -1, εAB = 1, as constants, and the interactions εAS as positive. This assignment ensures that the solvent is good to the B block and poor to the A blocks, and that the A and B blocks are immiscible. On the other hand, the block lengths n, the interaction parameters εAS, or the copolymer concentration cp, are varied systemically to examine their effects on the self-assembled aggregates.
Results and Discussion In this section, simulation results are presented in the form of morphology diagrams. The morphology diagrams are displayed in terms of the interaction parameter εAS and the copolymer concentration cp (Figures 1 and 2), or in terms of εAS only (Figure 3), for a given set of copolymer compositions. The mechanism of the morphological transitions with increasing εAS is elucidated by computing the contact numbers between different species (Figure 5). Finally, chain packing in different aggregates is investigated (Figures 6 and 7). Figures 1 and 2 present morphology diagrams with two sets of polymer compositions: (1) n = 8 (Figure 1) and (2) n = 10 (Figure 2). The first thing to notice is the rich variety of morphologies and morphological transitions exhibited in the diagrams. In Figure 1, a morphological sequence, spherical micelles (a) w rod micelles (b,c) w toroidal micelles (d-h) w vesicles (i), is observed with the increase of εAS. In the spherical micelles, most chains are with the middle B-block looped and the two outer A-blocks taking part of the same micellar core, hence the micelles are flowerlike. However, there does exist a small fraction of bridging chains with the outer A-blocks located in different micellar cores when cp is large. In this case, the spherical micelles are connected together through the bridging chains forming an extended network structure. On the other hand, the (40) Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. J. Chem. Phys. 1953, 21, 1087.
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Figure 1. Morphology diagram of triblock copolymers A8B8A8 in selective solvents for the middle B-block as functions of the interaction parameter εAS and the copolymer concentration cp. The same symbols represent similar morphologies. Representative snapshots of the micellar morphologies are shown. For clarity, a micellar structure, in which the B-block is removed, is shown separately on the right or below the corresponding snapshot. The labels in the snapshots correspond to (a) spherical micelles, (b,c) rod micelles, (d-h) toroidal micelles (in panel f, the micellar structures viewed from two directions are shown), and (i) vesicles. Color scheme in the snapshots: A (blue) and B (green).
morphology of toroidal micelles varies with cp value. When cp = 0.03, each toroidal micelle is a ring (d). When cp = 0.04, each toroidal micelle consists of a ring with a protruding tail (e), where the tail is a curved rod. When cp = 0.05, two other types of toroidal micelles are observed besides the one observed when cp = 0.04. In the first type, the toroidal micelle also can be considered as consisting of a ring with a tail, where the curved rod tail spans the ring so that both ends of the tail are connected with the ring (f). In this case, each toroidal micelle also can be considered as a cage consisting of three connected rings. In the second type, the toroidal micelle consists of a ring with two protruding tails (g), where each tail is a short rod. When periodic boundary conditions are considered in this case, rings are connected through rods, forming an extended ring-network structure. When cp is further increased to equal or larger than 0.06, complex cagelike toroidal micelles (h), in which the solvophobic A-blocks form ellipsoidal shells with holes, are observed, and they coexist with the ringnetwork structures. Furthermore, branched rods (c) are observed in a very narrow εAS region between the rod micelles and toroidal micelles. Comparing Figure 2 with Figure 1, we notice that the overall tendency of morphological transitions is similar in these two cases. However, there are several important differences between them. First, the same morphologies are shifted to the smaller εAS and larger cp values in Figure 2 than those in Figure 1. Second, in Figure 2, complex cagelike toroidal micelles never occur, whereas disklike micelles are observed in a narrow εAS range between the 4228 DOI: 10.1021/la903292f
ring-shaped toroidal or rod micelles and the vesicles when cp e 0.04. Besides these obvious differences in morphologies, the size of the regions occupied by the different micelles and the details in micelle structures are also different between the two cases. As an example for the difference in region size, it is noticed that the εAS range of the toroidal micelles is much larger in Figure 1 than that in Figure 2. As an example for the difference in details of the micelle structures, it is noticed that in ring-network structures, each ring can be with four protruding tails in Figure 2, whereas there are usually two protruding tails in Figure 1. To further investigate the influence of polymer compositions on the resulting aggregates, we also studied the system with n = 9. We find that the micellar morphologies obtained from this system are just between the above two cases, as shown in Figure 3. Figure 4a and 4b display the variation of the densities of segment A, B, and solvent with r, where r is the distance away from the center of mass of the micelle, and F(r), the average density over the spherical shell at r þ Δr for the vesicle or over the circular shell for the ring, respectively. We noted that the solvents are both inside and outside of the micelles. Two peaks for the curve of segment B are corresponding to the densities of segment B at the outer surface and the inner surface of the structure, respectively. We noted that the density of segment B at the outer surface is obviously lower than that at the inner surface for the vesicle, which is consistent with the result of Du et al.28 The aggregates shown in Figures 1-3 can be compared with previous observations for the similar block copolymers. Langmuir 2010, 26(6), 4226–4232
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Figure 2. Morphology diagram of triblock copolymers A10B4A10 in B-selective solvents as functions of εAS and cp. The color code is the same as that in Figure 1.
Figure 3. Typical morphologies of the triblock copolymers A9B6A9 in B-selective solvents as a function of εAS when cp = 0.04, using the same color scheme as that in Figure 1.
Flowerlike spherical micelles were observed experimentally for ABA triblock copolymers with small solvophobic end (A) blocks in B-selective solvents.30 ABA block copolymers with small solvophobic end blocks have been investigated for several years as systems forming associative networks of flowerlike micelles.31 All these results are consistent with our simulations, whereas vesicles and toroidal micelles were never observed or Langmuir 2010, 26(6), 4226–4232
predicted before for ABA-type triblock copolymers in a Bselective solvent. To elucidate the mechanism of the morphological transitions with increasing the interaction parameter εAS, the average contact numbers for the monomers are computed as a function of εAS. For a monomer, its nearest neighbors are one of the three species, that is, the A monomer, B monomer, and solvent. The total DOI: 10.1021/la903292f
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Figure 5. The variation of the average contact numbers for the A and B monomers with εAS. The regions of different micelles are also labeled in the figure, where SM means spherical micelles, RM means rod micelles, and TM means toroidal micelles.
Figure 4. The variation of the densities of segment A, segment B, and solvent with r in (a) a vesicle and (b) a ring from copolymer A8B8A8, where r is the distance away from the mass center of the vesicle or the ring, respectively.
contact number for each monomer should be the same as the number of nearest neighbors, which is 18 in our model. The average contact numbers for the A monomer with B monomers and solvents are defined as NAB and NAS, respectively. Similarly, the average contact number for the B monomer with solvents is defined as NBS. For the equilibrium morphologies of copolymer A8B8A8 with cp = 0.04, the variations of NAB, NAS, and NBS with εAS are plotted in Figure 5, and the regions of different micelles are also labeled. From Figure 5, it is clear that the contact numbers change with the morphologies. Figure 5 shows that among the micelle structures, vesicles have the smallest NAS, whereas spherical micelles have the largest NAS. The smallest NAS means the lowest total energy of the system at large εAS values, because the A-S contact is the major contribution to the total energy as εAS is large enough. Therefore, we can argue that the smallest NAS in vesicles is the reason that vesicles occur at large εAS values. On the other hand, the A-B and B-S contacts are the major contributions to the total energy, and the smallest NAB and largest NBS mean the lowest total energy of the system, as εAS is small enough. Therefore, we can argue that the smallest NAB and largest NBS in the spherical micelles is the reason that spherical micelles occur at small εAS values. At the intermediate εAS values, the competition between NAS, NAB, and NBS leads to the formation of the rod micelles and toroidal micelles. 4230 DOI: 10.1021/la903292f
Figure 6. Distribution P(j) for chains in the micelles from triblock copolymers A8B8A8.
Among the various aggregates, vesicles and toroidal micelles formed from amphiphilic block copolymers have attracted much attention, due to their great potential applications in the fields of drug delivery and nanotechnology. Vesicles have been observed in many amphiphilic block copolymer systems, whereas toroidal micelles are relatively rare. For the A-B two component systems, He and Schmid predicted ring-shaped and cage-shaped toroidal micelles from an amphiphilic diblock copolymer with a very short solvophilic block using a mesoscopic field-based simulation method.41 Very recently, Huang et al. observed ring-shaped toroidal micelles with uniform size from self-assembly of poly(isopreneblock-b-2-vinylpyridine) diblock copolymer solutions.18 Also for the A-B two component systems, Jiang et al. observed ring-shaped toroidal micelles and network structures from selfassembly of ABA-type triblock copolymers in an A-selective solvent.23-25 Furthermore, they have carried out self-consistent field theory calculations to account for the observed structures. In the past few years, the toroidal morphologies have been observed from the self-assembly of ABC triblock copolymers in dilute (41) He, X. H.; Schmid, F. Phys. Rev. Lett. 2008, 100, 137802.
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Article Table 1. The Variation of the Fraction of Bridge Chains in Copolymers A8B8A8 as Functions of εAS and cp εAS
cp = 0.03
cp = 0.04
cp = 0.06
1 2.5 3.5 4
0.026 0.044 0.048 0.115
0.064 0.022 0.072 0.147
0.106 0.0519 0.096 0.148
block A. As suggested by Huh et al.,47 the cos j is calculated with cos j ¼
ðrA1 -rB Þ 3 ðrA2 -rB Þ jrA1 -rB jjrA2 -rB j
ð1Þ
solution by Pochan et al.42-44 and Reynhout et al.,45 and of amphiphilic molecular dumbbells in aqueous solution by Kim et al.46 All these results indicate that toroidal micelles, just like spherical and rodlike micelles or vesicles, can be formed in most amphiphilic systems when the conditions are appropriate. From Figures 1-3, we notice that a small change in either polymer concentration, or polymer compositions, or polymersolvent interaction can influence the morphologies of the resulting aggregates. In a real experimental system, polymer concentration fluctuations, polydispersity of different blocks in block copolymers, or temperature fluctuations always exist, resulting in inhomogeneities in local polymer concentration, polymer compositions, or polymer-solvent interaction. On the basis of these considerations, we can assume that for a macroscale homogeneous solution it may show some inhomogeneous characteristics on the microscale due to the above-mentioned inhomogeneities. Our simulation results indicate that the inhomogeneities are factors that, at least partially, contribute to the coexistence of disparate morphologies even in one experimental system.21,22 Chain Packing. To gain insights into the chain packing in the aggregates, we calculated the distribution of j, P(j) for chains in the micelles, where j is the angle between the vectors from the center of mass of the middle B block to the centers of mass of each
where rA1, rB, and rA2 are position vectors of the centers of mass of the first end block A, the middle block B, and the second end block A, respectively. Figure 6 shows two typical P(j) curves for chains in different micelles. The large P(j) values at j < 60° in each curve implies that loop conformations are dominant among all the conformations in these micelles. On the other hand, the small peak at j > 120° in the solid curve indicates that there does exist a small fraction of bridge chains, whereas the dashed curve indicates that there hardly exist any bridge chains in the corresponding micelles. We find that when polymer concentration is high or the middle Bblock is relatively long, the solid curve is the typical distribution, whereas when the concentration is low, and the middle B-block is relatively short, the dashed curve is the typical one. We also find that the fraction of bridge chains increases with the increase of the polymer concentration or the length of the B-blocks. Furthermore, the fraction of bridge chains varies with micellar morphology, as shown in Table 1 for copolymers A8B8A8. The chain packing in the representative aggregates is illustrated in Figure 7. Figure 7a represents the case of spherical micelles. When the polymer concentration is low, or when the middle Bblock is short, each aggregate is an isolated flower-like micelle, where the B-block always takes a loop conformation so that the two end A-blocks become a part of the same micellar core.30 As mentioned earlier, there exists a small fraction of bridge chains in which the two end A-blocks may not necessarily return to the same micellar core when the polymer concentration is high or the middle B-block is relatively long. In Figure 7a, a bridge chain which spans two neighbor micellar cores is indicated. The chain packing in the cross sections along the rod axis of a rod or a ring-shaped toroidal micelle is similar to that in a spherical micelle. The two spheres shown in Figure 7a also can be considered as two cross sections with a small distance in the rod axis direction in a rod or part of a toroidal micelle. When the polymer concentration is high or the middle B-block is long, the angle j for the indicated chain can be larger than 90°, so that it is calculated as a bridge chain. Figure 7b represents the case of a vesicle. In this case, chains are also largely looped. However, there are a small fraction of chains with j > 90°. We find that these socalled bridge chains are usually with the B-block inside the shell of a vesicle as illustrated in Figure 7b.
(42) Pochan, D. J.; Chen, Z. Y.; Cui, H. G.; Hales, K.; Qi, K.; Wooley, K. L. Science 2004, 306, 94. (43) Chen, Z. Y.; Cui, H. G.; Hales, K.; Li, Z. B.; Qi, K.; Pochan, D. J.; Wooley, K. L. J. Am. Chem. Soc. 2005, 127, 8592. (44) Cui, H. G.; Chen, Z. Y.; Wooley, K. L.; Pochan, D. J. Macromolecules 2006, 39, 6599. (45) Reynhout, I. C.; Cornelissen, J. J. L. M.; Nolte, R. J. M. J. Am. Chem. Soc. 2007, 129, 2327. (46) Kim, J. K.; Lee, E.; Huang, Z. G.; Lee, M. J. Am. Chem. Soc. 2006, 128, 14022. (47) Huh, J.; Jo, W. H.; Brinke, G. Macromolecules 2002, 35, 2413.
Conclusion We predict that in solvents selective for the middle B-blocks, amphiphilic ABA triblock copolymers can self-assemble to form a rich variety of complex micelles. The predicted micelles are summarized in the morphology diagrams. Morphological transitions including vesicles and several types of toroidal micelles are predicted. We find that the resulting micellar morphology is sensitive to the copolymer composition, copolymer concentration, and
Figure 7. Schematic chain packing in different micelles: (a) spherical micelles; (b) vesicle. In each case, a bridge chain is indicated by an arrow.
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A-solvent interactions. Thus, we propose that the inhomogeneity in the local polymer concentration, polymer compositions, or polymer-solvent interaction can at least partly account for the coexistence of disparate morphologies observed in experimental system. We also find that in spherical micelles, there does exist a small fraction of chains with the middle B-block bridged and the outer A-blocks located in different micellar cores. Our simulation results enrich our knowledge of the phase behavior of ABA triblock copolymers in solvents selective for the middle (B) block. It should be noted that we adopted a coarse-grained model in which we assume that the size of the unit of the model is much larger than the atomic scale. Furthermore, we assume that the amphiphilic nature of the block copolymers is strong enough. Thus, the entropy loss from the loop formation of the middle
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block can be overcome by the energy preference, and micelles are formed in our considered cases. When the length of the copolymer is short or its amphiphilic nature is not strong enough, the results could be quite different from these predicted here. Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant No. 20474034 and No. 20774052), the National Science Fund for Distinguished Young Scholars of China (No. 20925414), by the Chinese Ministry of Education with the Program of New Century Excellent Talents in Universities (Grant No. ncet-05-0221) and the Program of the Joint- Research Foundation of Nankai and Tianjin Universities, and by Nankai University ISC. A.C.S. gratefully acknowledges the supports from the Natural Sciences and Engineering Research Council (NSERC) of Canada.
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